This site contains a Java based tool for creating graphs including surfaces, vector fields, implicit surfaces, surfaces in the spherical and cylindrical coordinate system, and space curves.
Type of Material:
Students can visualize and experiment with the graphs of surfaces in 3D. Implicit and parametric surfaces can also be plot using this tool.
A web browser with the java plugin installed.
Identify Major Learning Goals:
To create and explore surfaces, curves, and vector fields in 3D. In addition concepts of dot product and cross products are also explored through a series of practice questions.
Target Student Population:
Students in a third semester of multivariable or vector calculus course.
Prerequisite Knowledge or Skills:
The basics of functions of several variables.
Evaluation and Observation
Exploring Multivariable Calculus is an excellent tool which a student can use to visualize surfaces in 3D. A student can enter up to four equations where some of them can be in another coordinate system such as cylindrical or spherical or even implicit. The graphs are rendered in an easy to visualize manner. The wide variety of menu options allows a student to grab and turn the graphs until they are easy to visualize. They can also trace the point on the surface corresponding to a xy-point, and see the tangent planes, gradient vectors, etc. corresponding to it move on the surface as the location of the xy-point is altered. One can even plot the Taylor polynomials of varying degrees corresponding to a point of interest. There are demo scripts, e.g. surface intersections and points of discontinuity, that each illustrates a concept that students will see in multivariate calculus. The graphs can be enhanced if the student has 3D glasses.
Potential Effectiveness as a Teaching Tool
This is an excellent resource for both instruction and student exploration. Its easy to use menu features allow simple but effective rendering of 3D surfaces. It is certainly a well-designed applet page which can prove to be extremely useful to any student of multivariate calculus.
Ease of Use for Both Students and Faculty
There are a lot of in-built examples for students to explore. In addition, students can always create their own functions in any coordinate system (rectangular, cylindrical or spherical). The menus provide a lot of options to control the appearance of the graphs and also plot graphs related to the function such as tangent planes, vector fields to name a few.